1. Field of the Invention
The present invention relates to process control of a material on which a change in surface property occurs during such a process as thin film formation on a semiconductor, annealing of stainless steel plates, and galvannealing to thereby vary the emissivity of the surface.
2. Description of the Prior Art
In various material processing (such as thin film forming process on a semiconductor, annealing process of a stainless steel plate, and galvannealing process), the material temperature serves as an important parameter for satisfactory control of the process. As a technique to measure the material temperature in a non-contact manner, there is proposed radiation thermometry. In the radiation thermometry technique, the emissivity varies on account of changes in the physical properties such as oxidization and galvannealing on the materials surface and thermometric errors are produced as a result of the variation in the emissivity. Therefore, attempts have been made to correct for the variation in the emissivity to obtain a real temperature. As one of such techniques, there is two-color thermometry which performs radiation thermometry using two wavelengths.
In the two-color thermometry technique, the temperature measurement can be achieved fairly well when spectral emissivities for two wavelengths in use are virtually equal or have certain proportionality therebetween. However, when the surface condition of a hot matter suddenly changes due to oxidation occurring thereon, the spectral emissivities deviate from the aforesaid relationship and, the measurement accuracy extremely decreases. Much greater error is produced when a single-color radiation thermometer is used.
As techniques to overcome the above problems, there are proposed:
(a) a method disclosed in Japanese Patent Publication No. 3-4855; PA1 (b) a TRACE (Thermometry Re-established by Automatic Compensation of Emissivity) method disclosed in Tanaka and D. P. Dewitt: "Theory of a New Radiation Thermometry Method and an Experimental Study Using Galvannealed Steel Specimens", The Transactions of the Japanese Institute of Measurement and Automatic Control Engineers, Vol. 25, No. 10, pp. 1031-1037 (October 1989). PA1 .lambda..sub.i : measurement wavelength [.mu.m] PA1 .epsilon..sub.i : spectral emissivity for a measurement wavelength .lambda..sub.i [.mu.m] PA1 T: real temperature of the hot material surface [K] PA1 Si: brightness temperature of the hot material surface at a wavelength .lambda..sub.i [K] PA1 C2: (Planck's) second radiation constant, 1.4388.times.10.sup.4 [.mu.m.multidot.K]
Since both the above methods are basically the same, the former will be described below.
The spectral emissivity for radiation energy (light wave) emitted from a material in process is obtained by using Wien's approximation law. When wavelengths are .lambda..sub.1 and .lambda..sub.2, the emissivities are given by the following expressions (1) and (2) . By eliminating temperature T from these expressions, expression (3) can be obtained. EQU .epsilon..sub.1 =exp {C.sub.2 /.lambda..sub.1 (1/T-1/S.sub.1)}(1) EQU .epsilon..sub.2 =exp {C.sub.2 /.lambda..sub.2 (1/T-1/S.sub.2)}(2) EQU .epsilon..sub.1.sup..lambda.1 /.epsilon..sub.2.sup..lambda.2 =exp {C.sub.2 (1/S.sub.2 -1/S.sub.1)} (3)
where
The left side of the expression (3) is the ratio between "the wavelength power of spectral emissivities", which, will hereinafter be called "emissivity power ratio" for simplicity. The old two-color radiation thermometer is such that measures temperature on the assumption that the ratio between spectral emissivities (.epsilon..sub.1 /.epsilon..sub.2) is "1" or a constant, and because it does not respond to changes in the spectral emissivities, it produces a great measurement error.
Now, in Japanese Patent Publication No. 3-4855, the correlation function "f" of the emissivity power ratio to the spectral emissivity ratio (.epsilon..sub.1 /.epsilon..sub.2) as shown in the following expression (4), is determined in advance by measurement. In the temperature measurement, the spectral emissivity ratio is obtained from the emissivity power ratio calculated according to the above expression (3) by using the correlation function f, and the temperature T is obtained by calculation according to the following expression (5). EQU .epsilon..sub.1 /.epsilon..sub.2 =f(.epsilon..sub.1.sup..lambda.1 /.epsilon..sub.2.sup..lambda.2) (4) EQU T=(.lambda..sub.2 -.lambda..sub.1)/{.lambda..sub.1 .lambda..sub.2 /C.sub.2 .multidot.ln(.epsilon..sub.1 /.epsilon..sub.2)+(.lambda..sub.2 /S.sub.1)-(.lambda..sub.1 /S.sub.2)} (5)
In the measurement method using the above expressions, when it is applied to thermometry of a hot matter whose surface condition changes with the progress of oxidation reaction or the like, highly accurate temperature measurement can be attained provided that the measurement wavelengths that are selected are "insensitive" to changes of the surface status. However, when the emissivity power ratio of the selected wavelengths are sensitive to the change in the surface condition, the measurement accuracy greatly decreases as described below in detail.
As a concrete example where the spectral emissivities of selected wavelengths sensitively change responding to changes in the surface status of a hot matter, there is the case where the surface is oxidized and a translucent (at the measurement wavelength) oxide film is formed on the surface. In such a case, optical interference takes place in the translucent film formed on the surface and the spectral emissivity is thereby greatly reduced. In such case, the emissivity power ratio also greatly changes.
On such a phenomenon of sudden change of emissivity, Makino et al. give account in "Heat Transfer 1986", Vol. 2, Hemisphere (1986) pp. 577-582, on the basis of experiments and model calculation based on optical interference theories, that a drop (hereinafter called "valley") appears in the spectral emissivity spectrum at a short-wavelength zone when surface oxidation occurs and the valley is confirmed to move toward the longer-wavelength side as the oxidation progresses.
FIG. 1 to FIG. 5 are diagrams schematically showing an example of such a characteristic change in a spectral emissivity spectrum.
Referring to the diagrams, the axis of abscissas represents the spectral wavelength .lambda. and the axis of ordinates represents the emissivity .epsilon. and, further, the portion indicated by "valley" is a drop in the spectral emissivity spectrum.
FIG. 1 to FIG. 5 show changes in the spectral emissivity spectrum of the surface as an oxide film is progressively formed on a surface of such metal as stainless steel.
FIG. 1 shows an emissivity spectrum of the metal surface in a low temperature state where no oxide film is formed. FIG. 2 shows an intermediate temperature state where an oxide film is not yet formed. FIG. 3 shows an intermediate temperature state where an oxide film has started to formed. FIG. 4 shows a state of the same temperature and having the oxide film growing thereon. FIG. 5 shows a state of a high temperature and having a thick oxide film formed thereon.
The occurrence of the valley is considered chiefly due to optical interference caused by an oxide film. Makino et al. obtained spectral emissivity spectra through model calculation based on interference theories and report that results of the calculation and experimental results concur well with each other.
Accordingly, the phenomenon of the change in the spectral emissivity spectrum can be considered to occur because radiation energy of a spectral wavelength band on the order below the thickness of the oxide film is selectively trapped in the oxide film. More specifically, interference or multiple reflection in the oxide film causes remarkable energy attenuation in a uniquely selected radiation and the valley moves from short wavelength side to long wavelength side because the uniquely selected wavelength band moves as the oxide film becomes thicker.
Since the emissivity ratios change as the spectral emissivity spectra change with the passage of time as described above, it is natural that measurement errors are produced in the old type two-color radiation thermometer and measurement errors are equally produced even in the above described improved type two-color thermometer according to Japanese Patent Publication No. 3-4855 because of difficulty in calculating expressions used therein.
The reason is, while the calculation in the improved type two-color thermometer using near-by two wavelengths .lambda..sub.1 and .lambda..sub.1x requires that a correlation between the two spectral emissivities .epsilon..sub.1 and a .epsilon..sub.1x is determined as a regression function in advance from experimental data on an off-line basis, the regression procedure is subject to error. This will be briefly described below.
Supposing that actually measured data of spectral emissivities .epsilon..sub.1 and .epsilon..sub.1x are those obtained while the movement of the valley from short wavelength side to long wavelength side is taking place as in the spectral emissivity spectrum described above, the correlation of the emissivity .epsilon..sub.1 and the .epsilon..sub.1X changes as "positive correlation".fwdarw."negative correlation".fwdarw."positive correlation".
This will be understood easily if the changes in the values of the emissivities .epsilon..sub.1 and .epsilon..sub.1x corresponding to the near-by two wavelengths .lambda..sub.1 and .lambda..sub.1x in FIG. 1 to FIG. 5 are traced. More specifically, when the low wavelength portion of the "valley" in the diagrams (the portion where the spectral gradient is negative) comes between the wavelengths .lambda..sub.1 and .lambda..sub.1x, the relative magnitude between the spectral emissivities .epsilon..sub.1 and .epsilon..sub.1x is reversed and positiveness and negativeness of the correlation are reversed.
The situation will be concretely shown in FIG. 6 and FIG. 7. The correlation before passing the valley (FIG. 6) and that after passing the valley (FIG. 7) are obviously completely reverse.
In Tanaka et al., "Seitetsu Kenkyu (in Japanese)", No. 339 (1990) PP. 63-67, it is shown that the .epsilon..sub.1 -.epsilon..sub.2 correlation graph is not one-valued, but there is formed a loop, as schematically shown in FIG. 8. This loop is supposed to be also due to radiation interference occurring in the oxide film.
Thus, there is a problem that occurrence of some measurement error is unavoidable even in the improved type two-color thermometer because, as described above, the correlative regression graph between the emissivities .epsilon..sub.1 and .epsilon..sub.1x cannot be simply determined.
When temperatures of stainless steel plate (SUS 430) with surface oxidation in progress thereon were measured with the above described improved type two-color thermometer, the maximum measurement error in the temperature range around 600.degree. C. was 15.degree. C. or so in its maximum and the standard deviation was 5.degree. C. or so.
As described above in detail, a radiation thermometer cannot accurately measure the surface temperature of a material in process on an on-line basis when the surface status of the material changes with the passage of time accompanied by a variation in the emissivity as in the case where a steel plate is continuously processed. Hence, there is a difficulty that the thickness of the oxide film cannot be controlled with high accuracy even if the heating temperature such as the furnace temperature or the manipulated variable such as the line speed is controlled with the surface temperature of the material in process used as an indirect controlled variable.
Even if it is assumed that the surface temperature could be accurately measured, the thickness of the oxide film does not necessarily accurately correspond to the temperature. Again, there is a difficulty that it is not ensured that the thickness of the oxide film will be controlled to a desired value when the measured temperature is used as the controlled variable.
Such a difficulty as above is also encountered when a surface property such as the galvannealing degree is controlled in a continuous process of galvanized sheet steel.
Further, since the above described method is that for measuring temperature, it is only applicable to control of temperature and not applicable to other various kinds of process control. While the ultimate control target in an actual process is the property of material (physical property), shape of material (film thickness), or the like, temperature is only an agent supporting the progress of the process. In reality, a reaction acceleration indirectly caused by temperature is controlled in the prior art. Therefore, a control system using the temperature as the controlled variable is wasteful in controlling such a factor as the property of material (physical property) and shape of material (film thickness) and it poses a problem when structuring a control system. A desired value as a film thickness, or a material status value should be used as the controlled variable. An example for this problem will be shown below.
In a silicon semiconductor surface process (LSI process), a silicon oxide film controlled to high accuracy (of the 10.sup.-1 -10.sup.-2 .mu.m) is formed on the silicon surface. Generally, the time variation of the formed film thickness d under a constant temperature is measured off-line, and in the actual process, the temperature and the reaction time are automatically controlled. With the increased degree of refining in the process being required, the accuracy of film thickness control becomes severer, and it is presumed that the process time and heat pattern requirements will become even more severe. In concrete terms, quick heating and short-time processing will be required such as in RTP (Rapid Thermal Process). In such a process, the above described temperature measurement on the basis of off-line data has its limitations. More specifically, an oxide film is produced when a material is heated under a constant temperature and the change in the film thickness causes a problem.
The fundamental problem here is that indirect control with "temperature" is being performed while the target of process control is "thin film thickness". Accordingly, after the processing, there are produced statistical process errors of film thickness. Since it is very difficult to directly measure the film thickness, it is frequently questioned whether there is any better variable for indirect control.
More specifically, it is ideal if the "thin film thickness" as the target of process control is directly measured, but it is very difficult to directly measure the film thickness on-line. A known art of an optical measurement technique such as ellipsocollimation utilizing polarized light is not applicable to the process under high temperature. Because of such difficulties, the yield rate of products going through the LSI total process is very low. As the main cause of such situation, the above described difficulty in the thin film formation process control has come to be recognized, and there have been great demands for a thorough solution of the problem.